It's mid-morning, and wild flowers smell fresh after the first rain for six weeks. I'm cycling out of the village of Thixendale and the narrow road climbs gently out of the valley beneath high slopes covered with may trees. Suddenly I command great swooping vistas of far-off hills and green fields punctuated with copses of summer-happy trees. The sky is enormous.

No wonder David Hockney loves this part of Yorkshire. "He was outside with his easel just last month," Steve, the landlord of Thixendale's Cross Keys (01377 288272, B&B £30pp), had told me at dinner the night before, "painting this terrace of houses and the pub."

But I'm not in the Yorkshire Dales or even the North York Moors but in the Wolds, least well-known of Yorkshire's three sisters. A great boomerang of chalky hills in sensuous curves, it perhaps it owes its Cinderella status to its unfashionable location in the east of the county, just above Hull. Yet when I rose to their modest summits – the highest is only 250m – I still felt I was on the roof of the world. In cycling terms, you get a lot of bang for your low-gear buck.

And the icing on the cake was that I was the very first punter to try the Yorkshire Wolds Cycle Route, a 146-mile circular romp around tiny back roads, a smidgeon of the Yorkshire Wolds Way and a short section of the popular Way of the Roses coast-to-coast ride, created by sustainable transport charity Sustrans.

For someone who does a lot of his cycling in a city, such quiet roads provide something of a head rush. A couple of miles from Beverley I found the road not just quiet but deserted. A glide through Market Weighton and Pocklington warmed my legs for the climb into the Wolds proper. Fairweather cyclists will be relieved to learn that the Alps this ain't. A long but quite leisurely hill drew me up to the village of Huggate, where Hockney spent two summers as a youth, stacking corn, cycling and "falling in love with this part of the world".

And it is a world of its own. Familiar in some ways – large arable farms dotted with fields of eye-stingingly bright rape – but with some indefinable Yorkshire thing going on. Perhaps it's the cool white stone cottages or the sense that, if the farmers here turned their backs for more than a second, the Wolds would revert to the wilderness and outlaw hide-out it once was.

Nowadays it's a hide-out for a surprising number of wild animals. I saw magnificent hares bounding around the fields, plus goldfinches, yellowhammers, grey wagtails and bullfinches. One hot afternoon, a pair of lapwings sprang up and berated me for some minutes for cycling too close to their nest. On another, a pair of roe deer sprinted across the road a few feet from my front wheel.

In between the bucolic reveries (a picnic by the stream in the village of Settrington will remain long in my memory), I visited two cracking country houses and a landscaped garden. At Georgian Sledmere (sledmerehouse.com), the Capability Brown-inspired estate is so immense I was told I could go on a 14-mile walk without ever leaving it. Burnby Hall Gardens (burnbyhallgardens.com) were created, I discovered, by a retired army major who, bored one evening at a dinner party, took his wife around the globe eight times in order to "have something to talk about". Artefacts garnered from their travels are on display, and million-gallon lakes are home to the National Collection of Hardy Water Lilies.

At Elizabethan Burton Agnes Hall (burtonagnes.com) I was excitedly informed that two recent visitors to the Norman house in the grounds had taken a photo that revealed the presence of the ghost of a young girl. I nodded, masking my scepticism, then was shown the photo. Sure enough, there was the spectral figure sitting on some stairs. Later on, in the gloaming, I took several pictures of the same spot. Disappointingly, the wraith refused to show.

The cliffs at Bempton Photograph: Dixe Wills

After two days of contented hill hopping, I dropped down to the coast. One could hardly wish for a more spectacular stretch than the RSPB reserve at Bempton Cliffs. More than 200,000 sea birds live on these 100m chalk precipices. I stared mesmerised at kittiwakes, gannets and fulmars below me. A friendly birder called Martin lent me his monocular and I spent a few minutes in the world of a razorbill busy plucking chalk from the cliff to make a high-rise nest. Gripped with pangs of hunger on witnessing such industry I retired to munch on a delicious veggie burger at the cliffs' eco-friendly food trailer.

A few breezy miles later I was in Bridlington, as unpretentious a seaside resort as you could wish for and near neighbour of Sewerby Hall. I resisted the zoo and the pitch-and-putt golf course but did nose around the bijou museum dedicated to local girl and doomed flying ace Amy Johnson, before heading back to Burton Agnes village and my bed at the boutique Blue Bell (01262 490050, bluebellhotel.net, doubles from £65).

Accommodation on the route is plentiful enough. I plumped for two pubs, a small hotel (Wrangham House at Hunmanby, near Filey, 01723 891333, wranghamhouse.com, doubles from £95) and a former Dominican friary that now serves as Beverley's youth hostel (0845 371 9004, yha.org.uk, dorm beds £14.40). "It dates from 1330," I was told by Helen the warden as I arrived, "but your room's in the modern part." My heart sank. "When was that built?" I asked. "Oh, 1560. Your room's haunted, by the way."

I was having dinner at the Westwood restaurant (01482 881999, thewestwood.co.uk, three-course dinner £22.50) but to whip up an appetite, I climbed the 212 steps up the north tower of Beverley Minster (beverleyminster.org.uk). I breathed in the good Yorkshire air and gazed out across what were once marshes towards the Wolds – the gentlest, emptiest set of hills any cyclist could wish for.

• Singles London-Doncaster with East Coast (eastcoast.co.uk) cost from £9.35 booked online. Doncaster to Beverley return £24 with northernrail.org. Railway stations on the route are (clockwise): Beverley, Malton, Hunmanby, Bempton, Bridlington, Driffield, Hutton Cranswick. For more accommodation see visithullandeastyorkshire.com. A map of the route can be purchased from Sustrans (sustrans.org.uk) for £6.99. Big Skies Bike Rides are eight new one-day rides starting from towns on the Yorkshire Wolds route, see Visit Hull and East Yorkshire.